1. Field of the Invention
This invention relates to a timing recovery method and apparatus for symbol synchronization that overcomes timing problems encountered in general continuous phase modulation schemes.
2. Discussion of the Related Art
In March of 1981, T. Aulin, N. Rydbeck and C. Sundberg described a constant envelope modulation scheme as a method of continuous phase modulation at pages 196 through 225 of Vol. 29 of the IEEE Transactions on Communications. The method is plagued by synchronization problems created by the inexact timing recovery methods available in tha analog realm used. The problems were partially rectified by the work of B. Lankl and K. Friederichs which provided a digital phase detector that was independant of the carrier phase. Their efforts were presented on Nov. 15, 1995 and published in Vol. 2 of the IEEE Global Telecommunications Conference of that date.
The Lankl and Friederichs method for symbol synchronization is illustrated in FIG. 1. The modulation phase is detected by converting the sampled output of a quadrature receiver to a phase angle. The phase is delayed by the time between symbol starts and then subtracted from the current phase. This differencing removes the effects of residual carrier in the sampled values.
A nonlinear operation is performed on the differenced phase by computing the cosine of the scaled difference. The value of the scaling factor depends on the specific modulation being employed. The output of this nonlinear operation is multiplied by the value of a cosine function with a period equal to the symbol rate. The output of the mixing is an error signal that controls the phase locked loop by adjusting the oscillator that determines the sampling times in the quadrature receiver.
In Lankl and Friederichs, for modulations in which the phase is piecewise linear, the interpolation filter allows for digitization at a rate that is twice the rate at which new symbols are added to the data stream.
A. D""Andrea, U. Merigali, and M. Morelli developed a method for recovery of symbol timing which was published at pages 1362 through 1372 of Vol. 10 of the IEEE Transactions on Communications, October 1996. The method considers an optional statistical estimator and makes a series of approximations thereto to obtain an easily implemented approach. Because of the series of approximations, the final method is not optimal.
The primary objective of the invention is to provide a new method for timing recovery and symbol synchronization in a continuous phase demodulator that overcomes the problems of symbol synchronization for a general continuous phase modulation system.
The method is linear in the phase up to an inverse tangent function error detector. This linearity makes possible the application of the method of the invention in cases where the modulation is not binary.
In the method, the symbol phase error is determined by the output of a complex filter which must have an output magnitude that is nonzero if the phase is to be determined. The magnitude depends on the amount of overlap of the Fourier transform of a phase modulation function with a replica of the transform shifted by {fraction (2xcfx80/T)} where T is the time interval between symbol starts. Thus some of the energy in the phase modulation function must lay at frequencies that are more than half of the symbol rate or no overlap will exist.
In an example presented here, the error filter has been designed for a modulation function which is nonzero over an interval that is 16 times the time between successive symbol starts. It is assumed that 4 samples are collected during the time between each symbol start so that the length of the modulation is 64 samples.
The imaginary part of the filter output is zero at every offset that corresponds to an integral number of symbol start intervals. This is the basis for the symbol phase error.
The symbol synchronization procedure is independent of the modulation index and the size of the symbol set. There is no constraint on the modulation index to be a rational value.
In addition to tracking, acquisition of the symbol phase and frequency are also achieved by the methods of the invention.
The symbol phase synchronization procedure described hereby is tolerant to the presence of unremoved carrier phase. Such a phase will be present if the LO signal does not exactly match the carrier frequency in the I.F. channel input. The carrier phase tolerance comes about because the error detection filter produces a zero response for a DC input.